= Quartic hilltop inflation
{title2=$n_s\simeq1-3/N$}
Near a flat quartic maximum, $V\simeq\alpha\sigma^4-3\alpha\phi^4$. With <reduced Planck mass> $M$, the <slow-roll approximation> gives $N\simeq\sigma^4/(24M^2\phi_N^2)$, $\eta_V\simeq-3/(2N)$ and $\epsilon_V\simeq\sigma^4/(192M^4N^3)$. Hence $n_s\simeq1-3/N$, $n_T\simeq-2\epsilon_V$, and $\mathcal P_{\mathcal R}\simeq8\alpha N^3/\pi^2$. The result is dominated by the near-maximum part of the trajectory; extending slow roll to a distant minimum is unnecessary.
// Target: cosmic-inflation.bigb
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